M6 6.PFA.4 Inequalities

Answer explanation

The inequality x < -3 can be rewritten as -3 > x, which is equivalent. The other options either reverse the inequality or change the relationship, making -3 > x the correct choice.

Tags

VA.6.PFA.4.a

Which of the following linear inequalities represents the condition: "A number is at most 7"?

Answer explanation

The phrase 'at most 7' means the number can be 7 or any number less than 7. This is represented by the inequality x ≤ 7, which includes 7 itself. The other options do not satisfy this condition.

Tags

VA.6.PFA.4.b

• A person has more than 4 apples.

• A person has at most 4 apples.

• A person has less than 4 apples.

• A person has exactly 4 apples.

Answer explanation

The inequality x > 4 indicates that x must be greater than 4. Therefore, the correct contextual situation is that a person has more than 4 apples, which aligns with the inequality.

Tags

VA.6.PFA.4.c

• 3

• 2

• 4

• 5

Answer explanation

The inequality x ≤ 2 means x can be any number less than or equal to 2. Among the choices, only 2 satisfies this condition, as 3, 4, and 5 are greater than 2.

Tags

VA.6.PFA.4.d

• -2

• -1

• 0

• -3

Answer explanation

The inequality x > -1 means x can be any number greater than -1. Among the choices, 0 is greater than -1, making it a valid solution. The other options (-2, -1, -3) do not satisfy the inequality.

Tags

VA.6.PFA.4.e

Write a linear inequality to represent the condition: "A number is no less than 10."

Answer explanation

The phrase 'no less than 10' means the number must be 10 or greater. This is represented by the inequality x ≥ 10, which includes 10 itself. The other options do not satisfy this condition.

Tags

VA.6.PFA.4.b

• Yes, 6 satisfies the inequality.

• No, 6 does not satisfy the inequality.

• Cannot be determined.

• 6 is not a valid number for this inequality.

Answer explanation

To check if 6 satisfies the inequality x ≥ 5, substitute 6 for x. Since 6 is greater than 5, the inequality holds true. Therefore, the correct answer is: Yes, 6 satisfies the inequality.

Tags

VA.6.PFA.4.d

• -1

• 0

• -3

• 1

Answer explanation

The inequality x ≤ -2 includes all numbers less than or equal to -2. Among the choices, -3 is the only number that satisfies this condition, as -3 is less than -2. Therefore, -3 is part of the solution set.

Tags

VA.6.PFA.4.e

Match the graph with its inequality.

• a < 11

• a > 11

• a ≥ 11

• a ≤ 11

Answer explanation

The graph shows a solid line at 11, indicating that 11 is included in the solution set. This corresponds to the inequality a ≥ 11, meaning a can be 11 or any value greater than 11.

Tags

CCSS.6.EE.B.8

What inequality does the number line graph represent?

• x ≤ 4

• x ≥ -4

• x < -4

• x < 4

Answer explanation

The number line graph shows an open circle at -4 and shading to the left, indicating that x is less than -4. Therefore, the correct inequality is x < -4.

Tags

CCSS.6.EE.B.8